Hmm I wonder how much a boring company tunnel would cost... [snippage of good stuff] At $10 million per mile that's $300 million. Double it to make a loop to allow for bi directional travel. $600 million.
Disclaimer: The "napkin math" analysis below has been made by someone who has never even visited New Zealand. Some of my assumptions may therefore be entirely wrong.
Keep in mind that's for a single lane of traffic going each direction. How much throughput would that allow, and would that create a daily traffic jam? What would be a realistic transit time of the tunnel during a typical rush hour, given the number of people trying to use it every day?
Let's say, for the sake of argument, that a car enters/ exits the system once every 1.25 seconds. (Based on my personal driving experience, that's a realistically close -- although quite unsafe -- average spacing of cars traveling in dense traffic.) Let's assume a 1.75 hour window for "rush hour" traffic. (90 minutes might be more realistic, but let's err on the side of being generous.) One car every 1.25 seconds for (60 x 60 x 1.75) 6300 seconds yields 5040 cars.
The population of New Zealand's north island was estimated at 3.67 million in 2017; the population of the south island was estimated at 1.038 million back in 2011. I see per Wikipedia that the two major cities in New Zealand are both on the North Island. I therefore conclude -- perhaps wrongly, but it seems a reasonable conclusion -- that most of the industry and commercial buildings are on the north island, and that therefore the percentage of people traveling from the north island to the south island to work, and back north to go home, is probably a fairly low percentage of the north island's population. Therefore I'm going to ignore that portion of the traffic, assuming it at least won't be any greater than that going the other way. I'm going to consider just the traffic originating from the south island; presumably a larger percentage of people living there would be commuting to the north island for work, and back south to go home.
So, how many cars are there on New Zealand? Mr. Google says there were 3,858,000 vehicles in New Zealand in 2015. I'm going to make another assumption, which again is almost certainly not accurate: I'm going to assume the distribution of cars between the north and south islands is the same as the population distribution. If 77% of the cars are on the north island, that means ~34% are on the south island, or ~1,327,000.
5040 cars yields 0.38% of all the cars on the south island.
Sorry, Gooki, but unless I've made a serious mistake in my reasoning or math somewhere, then just one lane of traffic ain't gonna cut it. 10 "Boring Co." tunnels, yielding 10 lanes of traffic, would get you up to a capacity of ~3.8% of the cars on the south island... which I would guess still wouldn't be even close to being adequate to handle rush hour traffic.
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Addendum:
On the other hand, Wikipedia's article on the "Interislander" ferry service at New Zealand says the ferries handle about 230,000 vehicles per year, which averages only 630 per day, and that would be going both ways. Compared to that, a tunnel able to handle 5040 cars per day going north in the morning, and the same number going south in the evening, would be much more than adequate.
I guess the real question is just how much having a traffic tunnel between the islands would increase traffic. From my brief reading about the service, it looks like ferry fees are pretty steep, so at least in theory, the ability to drive from one island to the other would increase traffic dramatically, unless the tolls for using the traffic tunnel were similarly exorbitantly high.
